SOLUTION: A farmer drives a tractor from one town to another a distance of 120 kilometers. He drives 10 kilometers faster on the return trip cutting an hour off the time how fast does he dri

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Question 1051270: A farmer drives a tractor from one town to another a distance of 120 kilometers. He drives 10 kilometers faster on the return trip cutting an hour off the time how fast does he drive each way?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for the 1st trip
+t+-+1+ = time in hrs for the 2nd trip
Let +s+ = speed in km/hr for the 1st trip
+s+%2B+10+ = speed in km/hr on the 2nd trip
-------------------------------------------
For 1st trip:
(1) +120+=+s%2At+
For 2nd trip:
(2) +120+=+%28+s%2B10+%29%2A%28+t+-+1+%29+
-----------------------------
(2) +120+=+s%2At+%2B+10t+-+s+-+10+
(2) +120+%2B+10+=+t%2A%28+s+%2B+10+%29+-+s+
and
(1) +t+=+120%2Fs+
Substitute (1) into (2)
(2) +130+=+%28+120%2Fs+%29%2A%28+s+%2B+10+%29+-+s+
Multiply both sides by +s+
(2) +130s+=+120%2A%28+s+%2B+10+%29+-+s%5E2+
(2) +130s+=+120s+%2B+1200+-+s%5E2+
(2) +s%5E2+%2B+10s+=+1200+
Complete the square
(2) +s%5E2+%2B+10s+%2B+%2810%2F2%29%5E2+=+1200+%2B+%2810%2F2%29%5E2+
(2) +s%5E2+%2B+10s+%2B+25+=+1225+
(2) +%28+s+%2B+5+%29%5E2+=+35%5E2+
(2) +s+%2B+5+=+35+
+s+=+30+
and
+s+%2B+10+=+40+
He drove 30 km/hr for the 1st trip and
40 km/hr for the 2nd trip
-----------------------------------
check:
(1) +120+=+30t+
(1) +t+=+4+ hrs
and
(2) +120+=+%28+30%2B10+%29%2A%28+t+-+1+%29+
(2) +120+=+40%2A%28+t+-+1+%29+
(2) +3+=+t+-+1+
(2) +t+=+4+ hrs
OK